It's been annoying since forever I have been using Ilustrator (CS6).
I will illustrate the problem with a gif
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Use the scale tool (hit s), not the black arrow tool. The scale tool does not actually care where you click, which allows you to use geometry as reference. This has some other benefits than just this use case. Just remember to hold shift if you want to scale in one direction only or uniformly. Its also more accurate then the scale handles as it can use actual geometry edges, with smart guides for the scale even for thick non orthogonal lines.
Also using scale tool does not necessitate zooming as it respects smart guides of your cursor so snap edge to edge. Once you get used to it you can easily do the thing you demo even without scaling.
Scale tool can additionally specify what point to scale around, this allows you to spread things form one corner to another etc. Also if you alt click you get a numeric input, with scale emitting form the clicked point. All in all a superior way to scale, get into habit of using it.
PS: Scale tool can do this because there is no ambiguity of what you want to do. The scaling in selection tool needs to use handles so to know which operation you want to do which can obviously get in the way of scaling if what you want to scale is near a handle dedicated to something else. So there is no way to have a generic tool that is better than the dedicated one.
PPS: same applies to rotatinon tool
Seemingly you are frustrated because you cannot see scaling handle of a bounding box when you have high zoom. You can move the object but instead of moving you want to drag it wider. The object is something more complex than a rectangle.
If you have Smart Guides =ON, no extras are needed, but that's true only if your drawing is sparse enough and the bounding boxes are not rotated.
A workaround: Draw a temporary vertical line which is at the right place and can be seen at the same time as you drag the bounding box scaling handle. Remove the line when you are ready. Often people have "guides" for that purpose. You can convert a line to guide by selecting it and then right clicking it. One of the options is "Make Guides"
Workaround 2: Let it move. Stretch the other edge backwards if there's a better reference. There is, at least if you make a temporary duplicate
EDIT: After OP edited the question, the simple answer is "no." I would still recommend using the transform panel and/or smart guides.
[Answer to the original question]
There is no way to scale by clicking and dragging handles when they are off screen. Manual scaling is done in reference to either a corner, side center, or object center handle. Handles center to the bounding box, not the screen.
I would recommend using the transform panel. It is more accurate, can be based off of a selected handle that is not on screen, and can be used at any zoom level.